Probability and Venn Diagrams

Scheme of work: GCSE Higher: Year 10: Term 1: Probability and Venn Diagrams

Prerequisite Knowledge

  • Compare and order fractions whose denominators are all multiples of the same number.
  • Identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths
  • Add and subtract fractions with the same denominator and denominators that are multiples of the same number

Success Criteria

  • Record describe and analyse the frequency of outcomes of probability experiments using tables and frequency trees.
  • Apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future experiments
  • Relate relative expected frequencies to theoretical probability,
  • Apply the property that the probabilities of an exhaustive set of outcomes sum to one; apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to one
  • Understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size
  • Enumerate sets and combinations of sets systematically, using tables, grids, Venn diagrams and tree diagrams
  • Construct theoretical possibility spaces for single and combined experiments with equally likely outcomes and use these to calculate theoretical probabilities
  • Calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions

Key Concepts

  • When writing probabilities as a fraction using the probability scale to show equivalences with the keywords
  • Discuss the effect of bias and sample size when comparing theoretical and experimental probabilities.
  • Use the random function on a calculator or spreadsheet to demonstrate simple randomisation.
  • When listing the outcomes of combined events ensure students use a logical and systematic method.
  • Branches on a probability tree have a sum of one as they are mutually exclusive.
  • Conditional probability is where the outcome of a future event is dependent on the outcome of a previous event.

Common Misconceptions

  • Writing probabilities as a ratio is a common misconception.
  • When creating Venn diagrams students often forget to place the remaining events outside the circles.
  • When listing permutations of combined events students often repeat events when they do not use a logical and systematic method.
  • Students often have difficulty completing Venn diagrams involving 3 intersecting circles.

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